<p>In this paper, we are concerned with the uniqueness and nonlinear stability of steady vortex rings for the 3D Euler equation. Employing Arnold’s variational principle for steady Euler flows together with the concentration-compactness principle of P.-L. Lions, we first establish a general stability criterion for vortex rings within rearrangement classes. This reduces the analysis of nonlinear stability for thin vortex rings to the question of their uniqueness. We then prove the uniqueness of a distinguished family of vortex rings with small cross-sectional radius and a polynomial-type vorticity distribution. These rings, which correspond to global classical solutions of the 3D Euler equations, have previously been constructed via several distinct methods in prior work. Our uniqueness result is obtained through a detailed asymptotic analysis of the vortex rings as they approach a circular filament, combined with the use of localized Pohozaev identities. As a consequence, the nonlinear stability of this family of vortex rings follows from the combination of our general stability criterion and the uniqueness theorem.</p>